The statistically unbounded τ-convergence on locally solid Riesz spaces

2019/12/16 by Abdullah Aydın, Aydın, Abdullah · 1 citation
Decision Sciences · Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1912.07178

openalex publication_date 2019/12/16 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

A sequence (x_n) in a locally solid Riesz space (E,τ) is said to be statistically unbounded τ-convergent to x∈ E if, for every zero neighborhood U, (1)/(n)|\k≤ n:| x_k-x|\wedge u∉ U\|→ 0 as n→∞. In this paper, we introduce this concept and give the notions st-u_τ-closed subset, st-u_τ-Cauchy sequence, st-u_τ-continuous and st-u_τ-complete locally solid vector lattice. Also, we give some relations between the order convergence and the st-u_τ-convergence.

Cited by

• Rough convergence on Riesz spaces

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• Statistical unbounded convergence in Banach lattices
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